Homework 1

Introduction

<<<<<<< HEAD:hw1.Rmd A section called “Introduction” where you provide a short summary of the structure of your homework.

In the following sections we, the group members, will both introduce ourselves and demonstrate our RMarkdown skills. The first section, called “Group Member”, contains a picture of every group member, our hobbies, our favorite quote, and a table. This section is also complemented with emoji’s and Giphy’s. The second section contains our RMarkdown syntax. We demonstrate a chunk option, simulating random samples, an histogram, equations, purple text, a button, and a color box.

The structure section called “Introduction” where you provide a short summary of the structure of your homework. >>>>>>> 6a52820e49e41422ab009880086def4cc5fd6613:hw1_Original.Rmd

Moreover, record a short video to introduce your group and include it in your RMarkdown document.

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Group Member

Amina

Hello ! I’m Amina Mohammed, I’m following my last semester of course before writing my thesis. I’m super excited to follow this class and i expect to learn a bunch of new tools in order to develop new skills. 😄

Apart from my student life, I love to express my creativity through poterry. I love the process of creating a beautiful, sculptural and functional pieces with my own hands. I will give an extra point to this activity for the feeling of accomplishment; it feels incredible. 😍💗

If i had to choose emoji to describe myself I would certainly be: ☕📚 🐱 🍱 🍰 🍿

My fav quote would be :

Words can be like X-rays, if you use them properly—they’ll go through anything. You read and you’re pierced.

—Aldous Huxley, Brave New World

You can find in the table bellow the list of all my classes this semester

Classes	Schedule
Supply Chain	Monday from 8h30 - 12h00
Programming tools in DS	Tuesday from 9h00 - 12h00
IMC	Tuesday from 14h15 - 18h00
Project in DA	Thurday from 8h30 - 12h00
Production Control	Thurday from 14h00 - 18h00 (7 first week)
Risk Analytics	Thurday from 14h00 - 18h00 (7 last week)

I don’t have class on Wednesday and Friday, But i have some hectic days starting from 8am to 6pm.

Edward Tandia

Hey there! I am Edward Tandia, currently pursuing a master degree in Business analytics. As my friend Amina, this is also my last “normal” semester before starting the master thesis. I’m looking forward to learning new skills and improve myself in programming with R. I am 100% motivated and I truly believe that this semester will be memorable. 😄

My Hobbies?? Well, I am quite an open mind actually. I love to discover new topics, do sport,improve myself regardless the subject. Basically, I always seek self-improvement. 😍💗

My favortie quote is :

Each problem has its own solution.

— my mum

If i had to choose one emoji to represent myself, it would be this one: 😈

Classes	Schedule
Supply Chain	Monday from 8h30 - 12h00
Programming tools in DS	Tuesday from 9h00 - 12h00
Text mining	Wednesday from 8h30 - 12h00
Individual Behavior in Digital Environments	Wednesday from 14h15 - 18h00
Project in DA	Thurday from 8h30 - 12h00

Joost Dijkstra

Salut! My name is Joost Dijkstra and coming from the Netherlands. I am doing my QTEM exchange here, which stands for Qualitative Techniques for Economics and Management. This program gave me a lot of freedom to pursue my interests in the quantitative field. Giving me the opportunity to follow this course.

Next to my academic life, I of course have hobbies. Although I have many, I think the one I am looking out for the most is skiing, as the season is almost starting. I love how it can be both strenuous and relaxing at the same time.⛷🎿

My favortie quote is :

Have you ever had a dream that you, um, you had, your, you- you could, you’ll do, you- you wants, you, you could do so, you- you’ll do, you could- you, you want, you want them to do you so much you could do anything?

— Stuttering meme kid

Some emoji’s that would describe me are: 🌞🍻🏑🚴

Time	Monday	Tuesday	Wednesday	Thursday	Friday
08:30 - 12:00		Programming Tools in Data Science	Text Mining
12:30 - 14:00				French Class
14:15 - 18:00	Data Mining & Machine Learning				Optimization Methods in Management Science

RMarkdown Syntax

1.Show an example where the chunk option cache = T leads to a misleading answer.

Caching option can be really usefull however it can sometimes lead to missleading. Indeed, if a code is time consuming due to long computations or plots that are taking too long to generate, we can use knitr caching to improve performance. However, if codes are linked between eachother, when we modify one we have to observe that the code with chunk cache option are also update, otherwise, the code will always take into consideration the old cache that we “register”.

2. Simulate 1000 random samples from an exponential distribution with mean \(\lambda = 1\) using the function rexp(). Store these 1000 values in a vector called x. Then, compute the empirical median, mean and variance of x. Are these results different from \(log(2)/\lambda\), \(1/\lambda\) and \(1/\lambda^2\) (their respective theoretical values)? Is this result surprising? Justify your answer.

To do so, we have use set.seed and rexp()function. We have the following table:

Empirical values with lambda = 1	x	log(2)/x	1/x^2
Median	0.624	0.693	2.57e+00
Mean	0.974	5.948	8.54e+03
Variance	0.994	4073.937	6.52e+10

3. Repeat the same experiment with \(\lambda = 5\), display the code in the HTML file and discuss the results.

Empirical values with lambda = 5	x
Median	0.142
Mean	0.204
Variance	0.042

WE have an exponential distribution We get close results :

4. Include a graph showing the histogram of x (make sure to include a caption to this figure). What happens if you increase the number of bins to 200?

hist(y,xlab='Values',main = 'Exp distribution with lambda = 5')

hist(y,breaks= 200, xlab='Values',main = 'Exp distribution with lambda = 5')

We notice that the histogram with bins equal to 200, is more accurate. It shows some volatility between values 0 - 0.4 and gaps between values 1-1.2. The overall trend is still right queued and downward.

5. Include the following equation: \[f(x;p,q) = \frac{ \Gamma(p+q)}{\Gamma(p)\Gamma(q)} x^{p-1}(1-x)^{q-1}, 0 < x < 1\]

6. Include the following in-line equation:

In line we have : \(\mathbb{P}\{t \in [0, T]: X(t) > u \ as \ u \to \infty \}\)

7. Include the following text in purple: “It is change, continuing change, inevitable change, that is the dominant factor in society today. No sensible decision can be made any longer without….”, Isaac Asimov.

“It is change, continuing change, inevitable change, that is the dominant factor in society today. No sensible decision can be made any longer without….”, Isaac Asimov.

8. Include a “Click here” button with hide/unhide functionality.

9. Include a “color box”” with some text.

    Hello ! We're the group f